Cramér - von Mises StatisticCompute the probability associated with the Cramer-Mises statistic: \(\mathrm{CM}_{Statistic} = \frac{1}{12n} + \sum\limits_{i=0}^{n-1}{(\frac{2 \cdot i + 1}{2n}-f_{i})^{2}} \\ \mathrm{when} \: 0 < f_{i} \leq f_{i+1} < 1, \, \mathrm{for} \; 0 \leq i \leq n-1 \)(f = cummulative distribution function of the distribution function being tested). Computation limitations:Sample size, n; 2 ≤ n ≤ 1000, not necessary an integer.Calculated value of the Cramer-Mises statistic, on the sample of size n, with at least five significant digits, CM; 0.01 ≤ CM ≤ 1.Return value:Probability to be observed a better agreement between the observed sample and the hypothetical distribution being tested.Is obtained with four significant digits.Limitation: 1.0E-11 ≤ min(p,1-p).Ref:Jäntschi L. The Cramér–Von Mises Statistic for Continuous Distributions: A Monte Carlo Study for Calculating Its Associated Probability. Symmetry 2025, 17(9), 1542.Jäntschi L. Small Samples' Permille Cramér–Von Mises Statistic Critical Values for Continuous Distributions as Functions of Sample Size. Data 2025, 10(11), 181.Calculation uses 18 coeficients obtained from a high resolution Monte-Carlo experiment.Compute for: | |